Finite Group Databasebeta

← C107×#10034 #41035998

Subgroups — C107×#10034 #41035998

Order 27392.

584 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3150C211yesmaximal, characteristic
2C107×#3103C212yesmaximal, complemented
3C107×#1985C211yesmaximal, characteristic, complemented
4C107×#1480C212yesmaximal, complemented
5C107×#1275C211yesmaximal, characteristic, complemented
6C2×#135×C107—22no—
7#532×C107C2212yes—
8C2×C4×Q8×C107C2211yescharacteristic
9#497×C107—22no—
10#496×C107—22no—
11#481×C107—22no—
12#475×C107—22no—
13#460×C107—22no—
14#448×C107—22no—
15C4×SD16×C107—24no—
16#431×C107C2212yes—
17C2×C4⋊C8×C107C2211yescharacteristic
18C2×#97×C107C2211yescharacteristic
19#336×C107—22no—
20D4⋊C8×C107—24no—
21C2×#41×C107—22no—
22C22×Q8×C107D411yescharacteristic
23#135×C107—44no—
24#135×C107—44no—
25C2×Q16×C107—22no—
26C2×SD16×C107—24no—
27C2×SD16×C107—24no—
28C2×D8×C107—22no—
29C22×C8×C107—21no—
30C22×C8×C107D412yes—
31C4⋊Q8×C107D412yes—
32#127×C107D412yes—
33#124×C107—22no—
34#121×C107—22no—
35#121×C107—22no—
36C4×Q8×C107—22no—
37C4×Q8×C107—22no—
38C4×D4×C107—22no—
39C4×D4×C107—22no—
40C2×C4⋊C4×C107—21no—
41C2×C4⋊C4×C107D411yescharacteristic
42C2×C42×C107—21no—
43C2×C42×C107C2311yescharacteristic
44#106×C107—24no—
45C4⋊C8×C107—22no—
46C4⋊C8×C107—22no—
47#103×C107—24no—
48#102×C107—24no—
49C22⋊C8×C107—22no—
50#97×C107—22no—
51C4×C8×C107D414yes—
52#41×C107—44no—
53#41×C107—44no—
54C2×Q8×C107—22no—
55C2×Q8×C107—22no—
56C2×Q8×C107—42no—
57C2×D4×C107—22no—
58C2×D4×C107—22no—
59C2×D4×C107—22no—
60C2×D4×C107—42no—
61C22×C4×C107—21no—
62C22×C4×C107—21no—
63C22×C4×C107—42no—
64C22×C4×C107C2×D411yescharacteristic
65C22×C4×C107C2×D411yescharacteristic
66C22×C4×C107#4111yescharacteristic
67Q16×C107—44no—
68SD16×C107—48no—
69SD16×C107—48no—
70D8×C107—44no—
71C2×C8×C107—22no—
72C2×C8×C107—22no—
73C2×C8×C107—24no—
74C2×C8×C107—41no—
75C2×C8×C107—42no—
76C2×C8×C107SD1614yescomplemented
77C4⋊C4×C107—22no—
78C4⋊C4×C107—22no—
79C4⋊C4×C107—22no—
80C4⋊C4×C107—42no—
81C22⋊C4×C107—42no—
82C22⋊C4×C107—42no—
83C42×C107—41no—
84C42×C107—41no—
85C42×C107C2×D412yes—
86C42×C107C2×D412yes—
87C23×C107—42no—
88C23×C107#12111yescharacteristic
89Q8×C107—24no—
90Q8×C107—42no—
91Q8×C107—44no—
92D4×C107—44no—
93D4×C107—44no—
94D4×C107—44no—
95D4×C107—84no—
96C2×C4×C107—22no—
97C2×C4×C107—41no—
98C2×C4×C107—41no—
99C2×C4×C107—41no—
100C2×C4×C107—41no—
101C2×C4×C107—42no—
102C2×C4×C107—41no—
103C2×C4×C107—42no—
104C2×C4×C107—82no—
105C2×C4×C107—82no—
106C2×C4×C107#12012yes—
107C2×C4×C107#12011yescharacteristic
108C2×C4×C107#12112yes—
109C2×C4×C107#12711yescharacteristic
110C2×C4×C107C2×SD1612yes—
111C2×C4×C107AGL(1,ℤ/8)12yes—
112C8×C107—24no—
113C8×C107—44no—
114C8×C107—81no—
115C22×C107—21no—
116C22×C107—21no—
117C22×C107—82no—
118C22×C107—82no—
119C22×C107—82no—
120C22×C107#39211yescharacteristic
121C22×C107#46012yes—
122C4×C107—22no—
123C4×C107—22no—
124C4×C107—42no—
125C4×C107—82no—
126C4×C107—81no—
127C4×C107#45012yes—
128C4×C107#49211yescharacteristic
129C4×C107#49611yescharacteristic
130#10034C10711yesmaximal, characteristic, direct product factor, Sylow
131C2×C107—22no—
132C2×C107—162no—
133C2×C107#201011yescharacteristic
134C2×C107#201411yescharacteristic
135C2×C107#201711yescharacteristic
136#3150C2×C10711yescharacteristic
137#3103C2×C10712yescomplemented
138#1985C2×C10711yescharacteristic, complemented
139#1480C2×C10712yescomplemented
140#1275C2×C10711yescharacteristic, complemented
141C107#1003411yescharacteristic, direct product factor, Sylow
142C2×#135—22no—
143#532C22×C10712yes—
144C2×C4×Q8C22×C10711yescharacteristic
145#497—22no—
146#496—22no—
147#481—22no—
148#475—22no—
149#460—22no—
150#448—22no—
151C4×SD16—24no—
152#431C22×C10712yes—
153C2×C4⋊C8C22×C10711yescharacteristic
154C2×#97C22×C10711yescharacteristic
155#336—22no—
156D4⋊C8—24no—
157C2×#41—22no—
158C22×Q8D4×C10711yescharacteristic
159#135—44no—
160#135—44no—
161C2×Q16—22no—
162C2×SD16—24no—
163C2×SD16—24no—
164C2×D8—22no—
165C22×C8—21no—
166C22×C8D4×C10712yes—
167C4⋊Q8D4×C10712yes—
168#127D4×C10712yes—
169#124—22no—
170#121—22no—
171#121—22no—
172C4×Q8—22no—
173C4×Q8—22no—
174C4×D4—22no—
175C4×D4—22no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4D4×C10711yescharacteristic
178C2×C42—21no—
179C2×C42C23×C10711yescharacteristic
180#106—24no—
181C4⋊C8—22no—
182C4⋊C8—22no—
183#103—24no—
184#102—24no—
185C22⋊C8—22no—
186#97—22no—
187C4×C8D4×C10714yes—
188#41—44no—
189#41—44no—
190C2×Q8—22no—
191C2×Q8—22no—
192C2×Q8—42no—
193C2×D4—22no—
194C2×D4—22no—
195C2×D4—22no—
196C2×D4—42no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—42no—
200C22×C4C2×D4×C10711yescharacteristic
201C22×C4C2×D4×C10711yescharacteristic
202C22×C4#41×C10711yescharacteristic
203Q16—44no—
204SD16—48no—
205SD16—48no—
206D8—44no—
207C2×C8—22no—
208C2×C8—22no—
209C2×C8—24no—
210C2×C8—41no—
211C2×C8—42no—
212C2×C8SD16×C10714yescomplemented
213C4⋊C4—22no—
214C4⋊C4—22no—
215C4⋊C4—22no—
216C4⋊C4—42no—
217C22⋊C4—42no—
218C22⋊C4—42no—
219C42—41no—
220C42—41no—
221C42C2×D4×C10712yes—
222C42C2×D4×C10712yes—
223C23—42no—
224C23#121×C10711yescharacteristic
225Q8—24no—
226Q8—42no—
227Q8—44no—
228D4—44no—
229D4—44no—
230D4—44no—
231D4—84no—
232C2×C4—22no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—41no—
239C2×C4—42no—
240C2×C4—82no—
241C2×C4—82no—
242C2×C4#120×C10712yes—
243C2×C4#120×C10711yescharacteristic
244C2×C4#121×C10712yes—
245C2×C4#127×C10711yescharacteristic
246C2×C4C2×SD16×C10712yes—
247C2×C4AGL(1,ℤ/8)×C10712yes—
248C8—24no—
249C8—44no—
250C8—81no—
251C22—21no—
252C22—21no—
253C22—82no—
254C22—82no—
255C22—82no—
256C22#392×C10711yescharacteristic
257C22#460×C10712yes—
258C4—22no—
259C4—22no—
260C4—42no—
261C4—82no—
262C4—81no—
263C4#450×C10712yes—
264C4#492×C10711yescharacteristic
265C4#496×C10711yescharacteristic
266C2—22no—
267C2—162no—
268C2C107×#201011yescharacteristic
269C2C107×#201411yescharacteristic
270C2C107×#201711yescharacteristic
subgroupG/H
centerC2×C4×C107#127
commutator, Frattini, cosocleC2×C42C23×C107
socleC22×C107#392
prime radicalC107×#3150C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C107 ◁ C2×C42×C107 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C107×#3103C2semidirect
3. C107×#1985C2semidirect
4. C107×#1480C2semidirect
5. C107×#1275C2semidirect
76. C2×C8×C107SD16semidirect
130. #10034C107direct (N × H)
137. #3103C2×C107semidirect
138. #1985C2×C107semidirect
139. #1480C2×C107semidirect
140. #1275C2×C107semidirect
141. C107#10034direct (N × H)
212. C2×C8SD16×C107semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C107×#31502
C107×#31032
C107×#19852
C107×#14802
C107×#12752
#10034107